Saturday, March 16, 2019

KiwiSDR IQ data streams with >20.25 kHz bandwidth (5)

By now, gr-kiwisdr can coherently combine between 2 and 6 IQ data streams recorded from the same KiwiSDR.

Following an idea by WA2ZKD, the following test was made with DRM signals: three data streams were recorded, one centered on the DRM signal on 15120 kHz and two more centered on 15112.5 kHz and on 15127.5 kHz which were then coherently combined into a signal data stream. The GNURadio display is shown below:

Coherent combination of two IQ data streams using gr-kiwisdr.

Both, the WAV file centered on 15120 kHz, and the combined WAV file were successfully decoded by DREAM:

DREAM display

The SNR is comparable for both files, taking into account that it fluctuates by about ±0.5 dB:

DREAM waterfall display for the combined WAV file.

DREAM waterfall display for the WAV file recorded on the center frequency.

Only one slight difference was found in the SNR per carrier display: although the SNR per carrier is fluctuating quite a lot, for the combined WAV file there is a dip around the center which is not there for the WAV file recorded on the center frequency:

DREAM SNR per carrier display display for the combined WAV file.

DREAM SNR per carrier display for the WAV file recorded on the center frequency.

Wednesday, March 6, 2019

KiwiSDR IQ data streams with >20.25 kHz bandwidth (4)

This is a follow-up to this blog post.

The figure below summarizes how three IQ data streams with equal frequency offsets Δf are combined into a single IQ data stream with sampling frequency 4Δf:

Coherent combination of three KiwiSDR IQ streams

Note that the center frequencies are set to exact values, using GNSS timestamps to correct the local KiwiSDR oscillator, while the sampling frequencies of the IQ data streams are derived from the local KiwiSDR oscillator and are not exact. As a consequence the three IQ data streams are not coherent.

The three IQ data streams can be made coherent by 1) correcting for the frequency offsets and 2) aligning the relative phases.

1) Correcting for the frequency offset 

One way of describing this correction is by comparing a signal in stream#1 with frequency ΔF/2  and another signal in stream#2 with frequency -ΔF/2, taking into account that there are two different sampling rates: the true (GNSS aligned) sampling rate Fs and the sampling rate according to the state of the local KiwiSDR oscillator, F′:
         z1(n) = exp{2πinΔF/2F′s}
         z2(n) = exp{2πinΔF/Fs - 2πinΔF/2F′s} .
The beat offset signal is given by
         z1*(n) z2(n) = exp{2πinΔF(1/Fs - 1/F′s)} ,
and is used to correct for the frequency offset, where F′s is determined from the GNSS time tags in the KiwiSDR IQ streams.

2) Relative phase alignment 

Having corrected the frequency offsets, we are left with constant relative phase differences, Δϕ(0,1) and Δϕ(1,2). These global phase offsets are estimated by cross-correlating the overlapping parts of the spectra, indicated in yellow in the figure above. GNURadio makes it easy to do this, using a combination of freq_xlating_ccf and conjugate__cc and a simple block which estimates the phase difference between two vectors of IQ samples.

Because the overlaps between IQ streams are needed to estimate the phase offsets, recordings with should use the full available bandwidth.

The method described above has been implemented using GNURadio and is available as part of gr-kiwisdr. Please note that this is work in progress and might need further improvements.

As can be seen in the updated GRC flowgraph below, IQ stream sample alignment, the correction for coherence, and the PFB synthesizer were combined into a single GNURadio block, called coh_stream_synth. In addition, exp{iΔϕ(0,1)} and exp{iΔϕ(1,2)} are shown in a constellation diagram display in order to monitor phase coherence (=stable relative phases).

GRC flowgraph

Using the GNURadio PFB synthesizer with 2× oversampling (twox=True), edge effects at the boundaries between IQ data streams are avoided:

Coherent combination of three IQ streams @12 kHz into a single IQ stream @32 kHz.